Let $M$ be a compact manifold and $f:\,M\to M$ be a $C^1$ diffeomorphism on
$M$. If $\mu$ is an $f$-invariant probability measure which is absolutely
continuous relative to Lebesgue measure and for $\mu$$a.\,\,e.\,\,x\in M,$
there is a dominated splitting $T_{orb(x)}M=E\oplus F$ on its orbit $orb(x)$,
then we give an estimation through Lyapunov characteristic exponents from below
in Pesin's entropy formula, i.e., the metric entropy $h_\mu(f)$ satisfies
$h_{\mu}(f)\geq\int \chi(x)d\mu,$ where
$\chi(x)=\sum_{i=1}^{dim\,F(x)}\lambda_i(x)$ and
$\lambda_1(x)\geq\lambda_2(x)\geq...\geq\lambda_{dim\,M}(x)$ are the Lyapunov
exponents at $x$ with respect to $\mu.$ Consequently, by using a dichotomy for
generic volume-preserving diffeomorphism we show that Pesin's entropy formula
holds for generic volume-preserving diffeomorphisms, which generalizes a result
of Tahzibi in dimension 2